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Christian Lind Malte, Hans Malte, Lærke Rønlev Reinholdt, Anders Findsen, James W. Hicks, Tobias Wang (2017). ”Right-to-left shunt has modest effects on CO2 delivery to the gut during digestion, but compromises oxygen delivery.” Journal of Experimental Biology, 220, 531-536. https://doi.org/10.1242/jeb.149625

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Title: Right-to-left shunt has modest effects on CO2 delivery to the gut during digestion, but compromises oxygen delivery. Author(s): Christian Lind Malte, Hans Malte, Lærke Rønlev Reinholdt, Anders Findsen, James W. Hicks, Tobias Wang Journal: Journal of Experimental Biology DOI/Link: https://doi.org/10.1242/jeb.149625 Document version: Publisher’s PDF (Version of Record)

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SHORT COMMUNICATION

Right-to-left shunt has modest effects on CO2 delivery to the gut during digestion, but compromises oxygen delivery Christian Lind Malte1,*, Hans Malte1, Lærke Rønlev Reinholdt1, Anders Findsen1, James W. Hicks2 and Tobias Wang1

ABSTRACT digestion may be an exception. A combination of unique anatomical By virtue of their cardiovascular anatomy, reptiles and amphibians features of the crocodilian cardiovascular system (Hicks, 1998) can shunt blood away from the pulmonary or systemic circuits, but the combined with physiological measurements fostered the idea that – functional role of this characteristic trait remains unclear. It has been increased R L shunts serve to fuel the gastric mucosa with acidic suggested that right-to-left (R–L) shunt (recirculation of systemic proton-rich blood during digestion in alligators (Farmer et al., 2008; blood within the body) fuels the gastric mucosa with acidified and Gardner et al., 2011; Jones and Shelton, 1993). Central to this proposal is the observation that the crocodilian coeliac artery CO2-rich blood to facilitate gastric acid secretion during digestion. – appears as a continuation of the left aortic arch, which indicates that However, in addition to elevating PCO2,RL shunt also reduces the stomach is preferentially perfused with CO2-rich blood from the arterial O2 levels and would compromise O2 delivery during the increased metabolic state of digestion. Conversely, arterial P can right ventricle (e.g. Jones, 1996; Webb, 1979). In support for CO2 P also be elevated by lowering ventilation relative to metabolism (i.e. elevated (systemic) arterial partial pressure of CO2 ( CO2) reducing the air convection requirement, ACR). Based on a governing acid secretion, Farmer et al. (2008) reported slower mathematical analysis of the relative roles of ACR and R–L shunt digestion after surgical removal of the left aorta in alligators. However, a number of other studies show that growth is not affected on O2 and CO2 levels, we predict that ventilatory modifications are by similar procedures (Eme et al., 2009, 2010), and it is possible much more effective for gastric CO2 supply with only modest effects that the slower digestion stems from reduced perfusion of the on O2 delivery. Conversely, elevating CO2 levels by means of R–L gastrointestinal organs after occlusion of the left aortic arch (Hicks shunt would come at a cost of significant reductions in O2 levels. The and Wang, 2012). different effects of altering ACR and R–L shunt on O2 and CO2 levels are explained by the differences in the effective blood capacitance Although the cardiovascular system must simultaneously provide – coefficients. for O2 delivery and CO2 removal, the proposition that R L shunts assist gastric acid secretion has not included considerations of the KEY WORDS: Gas exchange, Heart, Mathematical model, Reptile, inexorable reduction in O2 delivery. R–L shunts cause large Shunting reduction in arterial O2 levels – whether expressed as partial pressure, O2 concentration or haemoglobin saturation (Wang and INTRODUCTION – P Hicks, 1996) while the effects on arterial CO2 are predicted to be The ability to shunt blood away from the pulmonary or systemic considerably smaller given the high capacitance coefficient for CO2 circulations is a defining character of the reptilian and amphibian in blood. An increased R–L shunt during digestion would therefore cardiovascular systems (Hicks, 1998). However, whilst much is also compromise O2 delivery, which seems undesirable given the known about the anatomical basis for central vascular shunts and fourfold elevation in O2 demands during digestion (Busk et al., their autonomic regulation, the functional role of bypassing one or 2000). In this context, it may be more prudent to elevate arterial P the other circulation remains as mysterious as it is debated (Hicks CO2 by means of ventilation [i.e. a lowering of the air convection and Wang, 2012). Thus, it remains uncertain as to whether this requirement (ACR) for CO2], a response that has been suggested to cardiovascular design is an exquisite adaptation to low ectothermic compensate for the rise in plasma bicarbonate during digestion (the metabolism and intermittent pulmonary ventilation, or merely an so-called ‘alkaline tide’; Hicks et al., 2000; Hicks and White, 1992; atavistic relict with no particular functional benefits (Hicks and Wang et al., 2001b). However, decreasing the ACR to elevate CO2 P Wang, 2012). levels will simultaneously lower the lung O2 and could negatively In several species of reptiles and amphibians, the right-to-left (R– impact O2 delivery. L) shunts (i.e. the direct recirculation of systemic venous blood into To address the compromise between adequate O2 delivery and the arterial systemic circulation) decrease whenever oxygen arterial acid–base status, we developed an integrated numerical demands are elevated (Hicks and Wang, 2012). However, in model that can be applied to amphibians and reptiles, to provide a crocodilians, an elevated oxygen consumption associated with quantitative comparison of the effects of R–L shunting and altered ventilation on blood O2 and CO2 levels.

1Zoophysiology, Department of Bioscience, Aarhus University, 8000 Aarhus C, MATERIALS AND METHODS Denmark. 2Department of Ecology and Evolutionary Biology, University of California, Irvine, CA 92697, USA. Fig. 1A illustrates the model of gas exchange for O2 and CO2 based on mass balances and relationships that express electro-neutrality in *Author for correspondence ([email protected]) blood compartments. The model does not include diffusion C.L.M., 0000-0002-7003-6370 limitations or spatial heterogeneities at tissues or lungs, and incorporates a thermodynamically correct description of the

Received 12 September 2016; Accepted 6 December 2016 Bohr–Haldane effect. Journal of Experimental Biology

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C The total concentration of CO2 in blood ( bCO2) is the sum of the List of symbols and abbreviations α P physically dissolved CO2 ( CO2 CO2) and the bicarbonate and ACR air convection requirement carbonate concentration, as quantified by the equilibrium constants C , concentration of CO or O in the pulmonary artery K K + PaCO2 2 2 of CO2 hydration ( 1 and 2) and the proton concentration ([H ], CPaO2 S which is related to O2): CPvCO2, concentration of CO2 or O2 in pulmonary venous return (i.e. ! C left atrium) PvO2 K1 K1K2 C , concentration of CO or O in the systemic arterial blood C ¼ a P 1 þ þ : ð10Þ SaCO2 2 2 bCO2 CO2 CO2 ½Hþ ½ þ2 CSaO2 H

CSvCO2, concentration of CO2 or O2 in systemic venous return (i.e. C right atrium) SvO2 Electro-neutrality in blood Hb haemoglobin

Lshunt gas exchange limitation imposed by shunts Equations that express electro-neutrality were derived by p number of Bohr-groups of haemoglobin conservation of charge, where electro-neutrality in a given blood i PACO2, partial pressure of CO2 or O2 in the lung gas compartment (subscript ) is given below: ! PAO2 P , P partial pressure of CO or O in a given compartment K K K K CO2 O2 2 2 ½ þ þ ¼ w þ a P 1 þ 2 1 2 P , P inspired partial pressure of CO or O H i SID þ CO2 CO2i þ ICO2 IO2 2 2 ½ ½ þ 2 _ H i H i ½H i QLR left-to-right shunt flow _ þ Qpul pulmonary blood flow þ b ð Þ ÞpC S ; ð Þ _ NB log(1/[H i pHiso Hb Hi 11 QRL right-to-left shunt flow _ Qsys systemic blood flow where SID is the strong-ion difference (Stewart, 1978), Kw is the Q_ total cardiac output tot ionic product of water, βNB is the non-bicarbonate buffer capacity, R–L right-to-left shunt pHiso is the pH of zero net charge of the buffer groups, SH is the Rperf blood convective/perfusive resistance p RQ respiratory quotient fractional saturation of haemoglobin with protons and is the number of Bohr-groups of haemoglobin. Rtot total resistance imposed to transport between tissues and the environment Rvent air convective/ventilatory resistance Shunt fractions and blood flows SH fractional saturation of haemoglobin with protons Total cardiac output (Q_ ) is the sum of pulmonary and systemic S HbO saturation tot O2 2 Q_ Q_ Q_ Q_ λ blood/gas partitioning coefficient flows ( pul and sys, respectively) and the shunt flows ( RLand LR) are given by total blood flow and the shunt fractions F ¼ Q_ =Q_ F ¼ Q_ =Q_ ( RL RL sys and LR LR pul). Given the desired general Mass balances applicability of the model to reptiles with (both R–LandL–R) intra- – For O : cardiac shunts, and not just crocodilians with central vascular (R L) 2 shunts, we derived the following expressions by mass balance, V_ ¼ Q_ ðC C Þ; ð Þ assuming uniformly well-stirred compartments with constant volume O2 sys SaO2 SvO2 1 where bi-directional shunts can occur independently: Q_ C þ Q_ C ¼ Q_ C þ Q_ C ; ð2Þ pul PvO2 RL PaO2 sys SaO2 LR SaO2 F _ _ 1 RL Q_ C þ Q_ C ¼ Q_ C þ Q_ C ; ð Þ Qpul ¼ Qtot ; ð12Þ sys SvO2 LR SaO2 RL PaO2 pul PaO2 3 F F 2 RL LR V_ b ðP P Þ¼Q_ ðC C Þ: ð4Þ 1 F A g IO2 AO2 pul PvO2 PaO2 Q_ ¼ Q_ RL : ð Þ sys tot 1 13 2 FRL FLR For CO2: However, given the present purpose we only considered V_ ¼ Q_ ðC C Þ; ð Þ CO2 sys SvCO2 SaCO2 5 unidirectional R–L shunts. Q_ C þ Q_ C ¼ Q_ C þ Q_ C ; ð Þ pul PvCO2 RL PaCO2 sys SaCO2 LR SaCO2 6 Numerical and analytical solutions Q_ C þ Q_ C ¼ Q_ C þ Q_ C ; ð7Þ sys SvCO2 LR SaCO2 RL PaCO2 pul PaCO2 Owing to the simplifying assumptions of the model, at steady-state V_ b ðP P Þ¼Q_ ðC C Þ: ð Þ P A ACO ICO PaCO PvCO 8 the pulmonary venous partial pressures of O2 and CO2 ( PvO2 and g 2 2 pul 2 2 P P PvCO2) are equal to the partial pressures in the lung ( AO2 and See Table 1 and the list of symbols and abbreviations for parameter P ACO2). The total system of 12 equations that express mass balance definitions. and electro-neutrality with 12 dependent variables (i.e. partial Concentrations and partial pressures in blood pressures and proton concentrations in the systemic and pulmonary The concentration of O in each blood compartment (C ) is the arterial and venous system for O2 and CO2) was solved numerically 2 bO2 in Mathematica (v.10.3, Wolfram Research). sum of haemoglobin (Hb)-bound O2 [product of blood Hb When blood capacitances of O2 and CO2 are assumed constant concentration (CHb), number of O2 binding sites (q=4) and S (approximately true for CO2 and applicable to O2 during hypoxia), saturation ( O2)] and the physically dissolved O2 [product of physical solubility (α ) and P ]: the system of equations can be solved analytically, leading to the O2 O2 following solutions: C ¼ qC S þ P a : ð Þ bO2 Hb O2 O2 O2 9 V_ R ¼ P P ; ð Þ O2 tot IO2 SvO2 14 To quantify the saturation of Hb with O and protons, the 2 V_ R ¼ P P ; ð15Þ Monod–Wyman–Changeux two-state model (Monod et al., 1965) CO2 tot SvCO2 ICO2 P R was incorporated where saturation is a function of both O2 and where tot is the total resistance imposed to transport from the blood/ – proton concentration to include the Bohr Haldane effect. tissues to the environment equal to the sum of the resistances Journal of Experimental Biology

532 SHORT COMMUNICATION Journal of Experimental Biology (2017) 220, 531-536 doi:10.1242/jeb.149625

A VA

A

Q pul Q Q pul Pa LR Pv

Q RL Sv Sa Q Q sys sys T

V V CO2 O2 B CD

1 120 60 0.8 )

90 2 40 O (mmHg) 60 0.6 saturation

(mmHg) ( S

2 2 2

O 30 CO 20 0.4 P P

0 HbO 0 V 25 0 V 25 V 25 A (ml STPD50 min 0.2 A (ml STPD50 min 0.2 A (ml STPD50 min 0.2 0.4 0.4 0.4 75 0.6 F 75 0.6 F 75 0.6 F RL 95 RL 95 RL –1 95 –1 0.8 –1 0.8 kg 0.8 kg kg –1 –1 –1 ) ) )

F P P S Fig. 1. Model illustration and 3D plots showing the effects of alveolar ventilation (and hence ACR) and RL on CO2, O2 and O2. (A) Illustration of the compartment model with abbreviations as follows: A, lung; Pa, pulmonary arterial blood; Pv, pulmonary venous blood; Sa, systemic arterial blood; Sv, systemic – venous blood; T, tissues. For other definitions, see the List of symbols and abbreviations and Table 1. (B D) 3D plots illustrate how (systemic) arterial PCO2 (B), PO2 (C) and HbO2 saturation (SO2; D) change as a function of the alveolar ventilation (and hence air convection requirement, ACR) and the right-to-left shunt fraction (FRL).

associated with blood convective/perfusive transport (Rperf ) and When only considering unidirectional R–L shunts, the total ventilation (Rvent): resistance simplifies to:

2 F 1 R ¼ R þ R : ð Þ R ¼ RL þ ; ð17Þ tot perf vent 16 tot Q_ b ð F Þ V_ b tot b 1 RL A g

Table 1. Parameter values used in simulations Parameters and variables Abbreviation Value Reference/notes _ Mean alveolar/effective ventilation VA Varied: 25– 100 ml STPD min−1 kg−1 −1 −1 Lung air capacitance coefficient βg 1/730 ml STPD ml mmHg _ −1 −1 Total cardiac output Qtot 150 ml min kg Right-to-left shunt fraction FRL Varied: 0.0–0.8 Left-to-right shunt fraction FLR 0 −1 Blood non-bicarbonate buffer capacity βNB 10.08 mmol l /pH unit Leads to similar total non-bicarbonate buffer capacity as excluding the contribution from Hb Bohr- reported for turtles (Weinstein et al., 1986) groups −1 Strong ion difference SID 11.42 mmol l Value required for initial condition of PCO2=35 mmHg,

PO2=100 mmHg, pH=7.2 −1 Haemoglobin concentration CHb 1.25 mmol l Half of typical human value Midpoint for pK pKm 7.3 Similar to human value Isoelectric pH value for haemoglobin pHiso 7.2 Similar to human value α −1 −1 Physical solubility of O2 in blood O2 0.00125 mmol l mmHg Christoforides and Hedley-Whyte, 1969 α −1 −1 Physical solubility of CO2 in blood CO2 0.032135 mmol l mmHg Reeves, 1976 _ ; _ −1 −1 CO2 production and O2 consumption VCO2 V O2 2 ml STPD min kg Journal of Experimental Biology

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A B 80 80 ↓ ACR Air-line

↓ ACR 60 60

40 ACR≈20

(mmHg) 40 2

CO F =0.8 F =0.8 ACR≈28

P RL RL F F ↑ F F 20 ↑ RL RL=0 20 RL RL=0

0 0 0 0.2 0.4 0.6 0.8 1.0 0 20 40 60 80 100 120 140 C D 80 80 Air-line

60 60 ↓ ACR 40 ↓ ACR

(mmHg) 40 ↓ ACR 2 CO P 20 20 ↑ F RL F ↑ RL 0 0 0 0.2 0.4 0.6 0.8 1.0 0 20406080100120140 HbO saturation (S ) P (mmHg) 2 O2 O2

E

80

60 (mmHg)

Air-line

2 40 ↓ ACR CO

P 20

0 0 150 0.2 HbO 100 0.4 F 2 saturation ( ↑ RL ) 0.6 50 (mmHg S P O 2 O 0.8 2 ) 1.0 0

P –P F P P S – Fig. 2. O2 CO2 diagrams of the solutions comparing the effects of altering ACR and RL on CO2, O2 and O2. (A D) Arterial PCO2 as a function of either HbO2 saturation (SO2)(A,C)orPO2 (B,D). In B and D, the dashed black line is the air-line with a slope given by a respiratory quotient (RQ) that ‘ ’ describes how PCO2 and PO2 change when altering ACR without shunts, and similarly in A and C, where the air-line becomes a curve. In B, the thick green curve originating at the dashed air-line/curve shows solutions when the right-to-left shunt fraction (FRL) is increased at a constant ACR. Note that to produce – –1 the same elevation in arterial PCO2 by means of R L shunt as by a moderate reduction in ACR (e.g. a reduction from 28 to 20 ml air ml CO2), the shunt fraction would have to increase to 0.8 with a concomitant large reduction in arterial PO2 and SO2 (A). (C,D) Solutions for different combinations of FRL (varied – – –1 0 0.8) and ACR (varied 12.5 50 ml air ml CO2), where the colour coding indicates increasing PCO2. Here, the thicker curves originating from the air-line/ curve show the effects of altering FRL at a given constant ACR. Conversely, the thinner curves originating from the thicker curves show the effects of altering ACR at a given FRL. (E) 3D plot summarizing the effects of altering FRL (thicker curves) and ACR (thinner curves) on both (systemic) venous and arterial blood. The plot is a combination of C and D, where PCO2 is on the vertical z-axis and SO2 and PO2 are on the horizontal x-andy-axes, and therefore also illustrates the effective O2 equilibrium curve. Note that when increasing FRL at a given ACR, the arterial and venous points move down the O2 equilibrium curve with only small elevations in PCO2. Conversely, reducing ACR at a given shunt leads to pronounced elevations of PCO2 but only moderate reductions in S .

O2 Journal of Experimental Biology

534 SHORT COMMUNICATION Journal of Experimental Biology (2017) 220, 531-536 doi:10.1242/jeb.149625

where βb is the blood capacitance coefficient for O2 or CO2. The left markedly reduced as the R–L shunt increases, whilst reductions in R S part on the right-hand side of Eqn 17 corresponds to perf and alveolar ventilation only moderately reduce O2 (Fig. 1C,D). Thus, =ð = Q_ b Þ simplifies to the normal perfusive resistance [1 1 2 tot b ] when our theoretical analysis reveals substantial differences on the there are no shunts, whereas the right part is Rvent. The perfusive influence of R–L shunt and ACR on arterial blood gases, and resistance (Rperf ) can be expressed as the normal resistance without predicts that ventilatory compensations are much more effective in R P shunts ( perf,FRL=0) multiplied by a function of the shunt fraction altering arterial CO2 than cardiac shunt patterns. [i.e. f(FRL)=½(2−FRL)/(1−FRL)]: The differences in the behaviours of O2 and CO2 upon changing shunt pattern or ACR are also illustrated in Fig. 2A–D, which shows R ¼ R f ðF ÞþR : ð Þ tot perf;FRL¼0 RL vent 18 P –P P S O2 CO2 diagrams and similar plots that relate CO2 and O2.In Fig. 2B, the dashed line describes steady-state solutions for lung While Rvent is the same for O2 and CO2, Rperf and hence Rtot differ given different β . The gas exchange limitation (Piiper and Scheid, gases and hence also the arterial blood gases in the absence of b cardiac shunts (i.e. the mammalian condition). In this case, 1972, 1981) imposed by R–L shunts (Lshunt) is given by 1 minus the total resistance without shunts (R , where F =0) divided by the reductions in ACR cause similar, but reciprocal changes in arterial tot RL P and P as predicted by the respiratory quotient (RQ; set to 1 in total resistance with shunts (i.e. R ): O2 CO2 tot the simulations). Conversely, an introduction of R–L shunt at a R ;F ¼ given ACR causes large reductions in arterial P while arterial L ¼ tot RL 0 ; O2 shunt 1 R P tot CO2 only increases moderately (full green curve in Fig. 2B). Thus, ð19Þ to produce the same elevation in arterial P by means of a R–L R þ R CO2 perf;FRL¼0 vent Lshunt ¼ 1 : shunt as by a moderate reduction in ACR (e.g. a reduction from 28 to Rperf;F ¼0 f ðFRLÞþRvent –1 RL 20 ml air ml CO2; Fig. 2B), the shunt fraction would have to This can also be expressed by the dimensionless ratio of the increase to 0.8, meaning that 80% of the systemic venous return normal perfusive to ventilatory resistance without shunts (w): bypasses the lungs (Fig. 2B). Such a large shunt fraction would P concomitantly reduce arterial O2 from more than 120 mmHg to less w þ S 1 than 30 mmHg (Fig. 2B) and reduce O2 from approximately 1.0 to Lshunt ¼ 1 ; ð20Þ w f ðFRLÞþ1 less than 0.5 (Fig. 2A). The complete solutions for different combinations of F (varied w RL where is given by the ventilation to perfusion ratio and the blood 0–0.8) and ACR (varied 12.5–50) for arterial blood are given in gas partitioning coefficient (λ=βb/βg) as follows: P Fig. 2C,D. The colour coding indicates increasing CO2 and the _ thicker lines originating from the air-line (the black dashed line/ R ;F ¼ V perf RL 0 A 1 P P S F w ¼ ¼ : ð21Þ curve) depict how O2, CO2 and O2 change as RL is altered at R 1= Q_ l vent 2 tot several constant levels of ACR. The thinner curves, originating from From Eqn 20 it is given that the transport limitation imposed by the thicker blood curves, represent solutions when ACR is altered at F shunts approaches zero whenw approaches zero (i.e. infinitely high a given constant RL. By combining the horizontal axes of Fig. 2C, blood flow and partitioning coefficient relative to ventilation). D, the possible solutions are summarized as a 3D diagram with P on the vertical z-axis and S and P on the horizontal x- and Conversely, the limitation approaches F /(2−F ) when w CO2 O2 O2 RL RL y x–y approaches infinity (i.e. infinitely high ventilation and low -axes (Fig. 2E). In this representation, the horizontal plane partitioning coefficient relative to blood flow). reflects the effective O2 equilibrium curve. Fig. 2E illustrates that F P increasing RL causes large reductions in O2 of the arterial and RESULTS AND DISCUSSION venous blood along the O2 equilibrium curve, leading to – S P The isolated and combined effects of R L shunts and ACR are pronounced O2 reduction with only moderate elevation of CO2. – P P F illustrated in 3D plots in Fig. 1B D, where arterial CO2, O2 and Conversely, reducing ACR at a given RL leads to a large elevation S – P S HbO2 saturation ( O2) are shown as functions of both R L shunt of CO2 with only moderate reductions in O2 (thinner upwards- fraction (FRL) and alveolar ventilation. It is immediately clear that bending curves in Fig. 2E). P – arterial CO2 increases most steeply when alveolar ventilation is The different effects of altering ACR and R L shunt on O2 and reduced (i.e. reduced ACR), but only moderately when FRL is CO2 is explained by the differences in blood capacitance P S β increased (Fig. 1B). Conversely, both arterial O2 and O2 are coefficients ( b) (alternatively expressed as differences in blood

R F V Fig. 3. Simplified analytic solution of the model perf, RL=0 A 1 ϕ == that illustrates the limitation imposed on gas R ½ Q λ L 1.0 vent tot exchange by shunts ( shunt, Eqn 21) as a 4 function of the right-to-left shunt fraction (FRL) for different values of the ratio of the perfusive 0.8 to ventilatory resistance without shunts (w, ϕ→∞ 3 Normoxia Eqn 22, colour coded). The asymptotic limitations ) 0.6 when w approaches infinity or zero are plotted. As a

shunt 2 O2 consequence of higher blood capacitance ( L 0.4 coefficient (βb) and hence blood/gas partitioning λ w Hypoxia coefficient ( ), for O2 is higher than for CO2 and 0.2 1 hence O2 uptake will be more limited by a given ϕ shunt.

Limitation imposed by shunt =0 CO 0 2 0 0.2 0.4 0.6 0.8 1.0 F R–L shunt fraction ( RL) Journal of Experimental Biology

535 SHORT COMMUNICATION Journal of Experimental Biology (2017) 220, 531-536 doi:10.1242/jeb.149625 gas partitioning coefficients, λ). This is illustrated in Fig. 3, showing Funding This study was funded by the Danish Research Council (Natur og Univers, Det Frie the limitation imposed on gas exchange by FRL (Eqn 21). Here, the ratio of the normal perfusive to ventilatory resistance without shunts Forskningsråd). w ( ) is varied from a physiologically relevant range for O2 and CO2 References (colour coded), and the asymptotic relationship between the Busk, M., Overgaard, J., Hicks, J. W., Bennett, A. F. and Wang, T. (2000). Effects of feeding on arterial blood gases in the American alligator Alligator limitation and FRL for w approaching infinity and w=0 is given by the black curve and the horizontal axis. Fig. 3 emphasizes that at a mississippiensis. J. Exp. Biol. 203, 3117-3124. Christoforides, C. and Hedley-Whyte, J. (1969). Effect of temperature and given shunt fraction, the gas species mostly limited by the shunt is hemoglobin concentration on solubility of O2 in blood. J. Appl. Physiol. 27, the one with the highest blood to air convective resistance (w) and 592-596. hence the lowest λ (i.e. lowest β ). Therefore, owing to the high β , Eme, J., Gwalthney, J., Blank, J. M., Owerkowicz, T., Barron, G. and Hicks, J. W. b b (2009). Surgical removal of right-to-left cardiac shunt in the American alligator CO2 is less limited by shunts than O2, although the differences may (Alligator mississippiensis) causes ventricular enlargement but does not alter become less distinct in deep hypoxia where the effective βb for O2 apnoea or metabolism during diving. J. Exp. Biol. 212, 3553-3563. increases. The same conclusion was made by Wagner (1979) when Eme, J., Gwalthney, J., Owerkowicz, T., Blank, J. M. and Hicks, J. W. (2010). Turning crocodilian hearts into bird hearts: growth rates are similar for alligators considering the effects of lung shunts on O2 versus CO2 exchange. with and without right-to-left cardiac shunt. J. Exp. Biol. 213, 2673-2680. Besides the differences in effects of shunts on O2 and CO2, Fig. 3 Farmer, C. G., Uriona, T. J., Olsen, D. B., Steenblik, M. and Sanders, K. (2008). also illustrates that the limitation in general is predicted to increase The right-to-left shunt of crocodilians serves digestion. Physiol. Biochem. Zool. when overall V_ =Q_ is high and vice versa. 81, 125-137. A tot Gardner, M. N., Sterba-Boatwright, B. and Jones, D. R. (2011). Ligation of the left If digestion is facilitated by supplying the gut with blood with aorta in alligators affects acid–base balance: a role for the R→ L shunt. Respir. higher CO2 levels, our model predicts that this is best mediated by Physiol. Neurobiol. 178, 315-322. Hartzler, L. K., Munns, S. L., Bennett, A. F. and Hicks, J. W. (2006). Metabolic and reducing ACR instead of increasing R–L shunt. Elevating CO2 – blood gas dependence on digestive state in the Savannah monitor lizard Varanus levels by increasing R L shunt would come at the cost of exanthematicus: an assessment of the alkaline tide. J. Exp. Biol. 209, 1052-1057. pronounced reductions in O2 levels, producing hypoxemia at a Hicks, J. W. (1998). Cardiac shunting in reptiles: mechanisms, regulation and physiological functions. Biol. Reptilia 19, 425-483. time at which O2 demand may be elevated fourfold above resting (e.g. Busk et al., 2000). Conversely, reductions of ACR entail Hicks, J. W. and Wang, T. (2012). The functional significance of the reptilian heart: new insights into an old question. In Ontogeny and Phylogeny of the Vertebrate much smaller reductions in O2 delivery, but provide for an Heart (ed. T. Wang and D. Sedmera), pp. 207-227. New York: Springer-Verlag. P Hicks, J. W. and White, F. N. (1992). Pulmonary gas exchange during intermittent effective elevation of CO2 that compensates for the alkaline tide during digestion (Wang et al., 2001a). Furthermore, these ventilation in the American alligator. Respir. Physiol. 88, 23-36. Hicks, J. W., Wang, T. and Bennett, A. F. (2000). Patterns of cardiovascular and postprandial reductions in ACR are well known in reptiles ventilatory response to elevated metabolic states in the lizard Varanus (Hicks et al., 2000; Overgaard et al., 1999; Secor et al., 2000) exanthematicus. J. Exp. Biol. 203, 2437-2445. Jones, D. (1996). The crocodilian central circulation: reptilian or avian? Verh. Dtsch. and PO remains high during digestion in all animals studied, 2 Zool. Ges. 89, 209-218. including alligators (Busk et al., 2000; Hartzler et al., 2006; Jones, D. R. and Shelton, G. (1993). The physiology of the alligator heart: left aortic Overgaard et al., 1999). flow patterns and right-to-left shunts. J. Exp. Biol. 176, 247-270. For many reptiles and amphibians, digestion is associated with Monod, J., Wyman, J. and Changeux, J.-P. (1965). On the nature of allosteric large elevations in oxygen demands and an increased need to transitions: a plausible model. J. Mol. Biol. 12, 88-118. – Overgaard, J., Busk, M., Hicks, J. W., Jensen, F. B. and Wang, T. (1999). secrete gastric acid with resulting challenges to blood acid base Respiratory consequences of feeding in the snake Python molorus. J. Comp. balance. Our theoretical approach clearly demonstrates that reliance Physiol. A 124, 359-365. on R–L shunting to meet the digestive demands conflicts Piiper, J. and Scheid, P. (1972). Maximum gas transfer efficacy of models for fish gills, avian lungs and mammalian lungs. Respir. Physiol. 14, 115-124. significantly with increased metabolic demands of the digestive Piiper, J. and Scheid, P. (1981). Model for capillary-alveolar equilibration with organs, and cannot provide adequate compensation for the alkaline special reference to O2 uptake in hypoxia. Respir. Physiol. 46, 193-208. tide. In contrast, ventilatory regulation, through reductions in ACR, Reeves, R. B. (1976). Temperature-induced changes in blood acid-base status: pH and P in a binary buffer. J. Appl. Physiol. 40, 752-761. addresses all the physiological challenges simultaneously, i.e. CO2 Secor, S. M., Hicks, J. W. and Bennett, A. F. (2000). Ventilatory and cardiovascular blood acid–base regulation, increased CO2 delivery to the gastric responses of a python (Python molurus) to exercise and digestion. J. Exp. Biol. mucosa without sacrificing O2 delivery. Thus, while our theoretical 203, 2447-2454. model obviously does not provide information on the actual Stewart, P. A. (1978). Independent and dependent variables of acid-base control. Respir. Physiol. 33, 9-26. physiological responses of living animals, it would certainly seem Wagner, P. (1979). Susceptibility of different gases to ventilation–perfusion that natural selection should favour efficient ventilatory regulation inequality. J. Appl. Physiol. 46, 372-386. Wang, T. and Hicks, J. W. (1996). The interaction of pulmonary ventilation and the on arterial PCO rather than the ineffective mean of regulation by 2 right–left shunt on arterial oxygen levels. J. Exp. Biol. 199, 2121-2129. central vascular shunts. Wang, T., Busk, M. and Overgaard, J. (2001a). The respiratory consequences of feeding in amphibians and reptiles. J. Comp. Physiol. A 128, 533-547. Competing interests Wang, T., Warburton, S., Abe, A. and Taylor, T. (2001b). Vagal control of heart rate The authors declare no competing or financial interests. and cardiac shunts in reptiles: relation to metabolic state. Exp. Physiol. 86, 777-784. Webb, G. J. (1979). Comparative cardiac anatomy of the Reptilia. III. The heart of Author contributions crocodilians and an hypothesis on the completion of the interventricular septum of This analysis results from numerous discussions over the past decade involving all crocodilians and birds. J. Morphol. 161, 221-240. the authors. C.L.M. constructed the model used in the manuscript on the basis of Weinstein, Y., Ackerman, R. A. and White, F. N. (1986). Influence of temperature previous simpler attempts. The manuscript was written by H.M. and T.W. with on the CO2 dissociation curve of the turtle Pseudemys scripta. Respir. Physiol. 63, continuous input and final approval of all co-authors. 53-63. Journal of Experimental Biology

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